Receding horizon quadratic optimal control: Performance bounds for a finite horizon strategy

Nevistic, V.; Primbs, James A.

doi:10.23919/ecc.1997.7082670

Cited by 20 publications

(20 citation statements)

References 10 publications

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“…However, no explicit bounds on stabilizing prediction horizons were given. The first explicit bound on a stabilizing prediction horizon was deduced in [28,30] for linear and in [10,39] for nonlinear systems, respectively. The main ingredient in the stability analysis was the knowledge of an upper bound of the optimal cost function.…”

Section: Introduction Model Predictive Control (Mpc)mentioning

confidence: 99%

The Role of Sampling for Stability and Performance in Unconstrained Nonlinear Model Predictive Control

Worthmann¹,

Reble²,

Grüne³

et al. 2014

SIAM J. Control Optim.

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Abstract.We investigate the impact of sampling on stability and performance estimates in nonlinear model predictive control without stabilizing terminal constraints or costs. Interpreting the sampling period as a discretization parameter, the relation between continuous and discrete time estimates depending on this parameter is analyzed. The technique presented in this paper allows us to determine the sampling rate required in order to approximate the continuous time suboptimality bound arbitrarily well and, thus, gives insight into the trade-off between sampling time and guaranteed performance.

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Section: Introduction Model Predictive Control (Mpc)mentioning

confidence: 99%

The Role of Sampling for Stability and Performance in Unconstrained Nonlinear Model Predictive Control

Worthmann¹,

Reble²,

Grüne³

et al. 2014

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…From the literature, it is well-known that this condition is satisfied for sufficiently long horizons N , cf. [1,12,19], and that a suitable N may be computed via methods described in [16,24,30]. The suboptimality index α in this inequality can be interpreted as a lower bound for the rate of convergence.…”

Section: Assumption 32mentioning

confidence: 99%

“…, N − 2, and u N (N − 1; x) = 0, cf. [24]. Now, we implement the Riccati feedback in the usual receding horizon fashion µ N (x(n)) := u N (0; x(n)) with N = 3 and evaluate the suboptimality bound from Theorem 3.3 along the closed loop.…”

Section: Example 41mentioning

confidence: 99%

Stability and performance guarantees for model predictive control algorithms without terminal constraints

Pannek

Worthmann

2014

Z Angew Math Mech

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A typical bottleneck of model predictive control algorithms is the computational burden in order to compute the receding horizon feedback law which is predominantly determined by the length of the prediction horizon. Based on a relaxed Lyapunov inequality we present techniques which allow us to show stability and suboptimality estimates for a reduced prediction horizon. In particular, the known structural properties of suboptimality estimates based on a controllability condition are used to cut the gap between theoretic stability results and numerical observations.

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“…A third approach uses a relaxed Lyapunov condition presented in [11] which can be shown to hold if the system is controllable in terms of the stage costs [8,10]. Additionally, this method allows for computing an estimate on the degree of suboptimality with respect to the infinite horizon controller, see also [15,19] for earlier works on this topic.…”

Section: Introductionmentioning

confidence: 99%

Performance of Sensitivity Based NMPC Updates in Automotive Applications

Pannek

Gerdts

2014

Mathematics in Industry

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In this work we consider a half car model which is subject to unknown but measurable disturbances. To control this system, we impose a combination of model predictive control without stabilizing terminal constraints or cost to generate a nominal solution and sensitivity updates to handle the disturbances. For this approach, stability of the resulting closed loop can be guaranteed using a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs. For the considered example, the proposed approach is realtime applicable and corresponding results show significant performance improvements of the updated solution with respect to comfort and handling properties.

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Receding horizon quadratic optimal control: Performance bounds for a finite horizon strategy

Cited by 20 publications

References 10 publications

The Role of Sampling for Stability and Performance in Unconstrained Nonlinear Model Predictive Control

The Role of Sampling for Stability and Performance in Unconstrained Nonlinear Model Predictive Control

Stability and performance guarantees for model predictive control algorithms without terminal constraints

Performance of Sensitivity Based NMPC Updates in Automotive Applications

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